Discussion of power-sum polynomials (Q1266953)
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scientific article; zbMATH DE number 1209946
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Discussion of power-sum polynomials |
scientific article; zbMATH DE number 1209946 |
Statements
Discussion of power-sum polynomials (English)
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11 January 1999
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Let \[ P_n(x)= {1\over n} \sum^{n-1}_{i=0} {n\choose i} B_ix^{n-i}, \] where \(B_0\), \(B_1, \dots\) are the Bernoulli numbers. It is well known that for \(x=2,3, \dots\) \[ P_n(x)= \sum^{x-1}_{i=1} i^{n-1}, \] i.e., \(P_n(x)\) is the power-sum polynomial. The author proves elementary properties (recursion formulas, symmetries, roots) of these polynomials in an elementary way which is helpful for the promotion of gifted pupils.
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recursion formulas
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Bernoulli numbers
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power-sum polynomial
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roots
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0.7653353810310364
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